#### Question:

Which system of linear inequalities has the point (2 ,1) in its solution set?

Posted By Admin @ November 26, 2022

Which system of linear inequalities has the point (2 ,1) in its solution set?

**Answer:**

**The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0**

**Step-by-step explanation:**

**Given: **Point ( 2 , 1 )

**To find:** System of Linear Inequalities which contain given point in

its solution set

**There are 2 lines passing through point ( 2 , 1 )**

So first we find the equation of both lines

**Equation of line using Two-Point form is given by,**

**Equation of line 1 passing through ( 0 , 2 ) & ( 4 , 0 )**

**....... (1)**

**Equation line 2 passing through ( 0 , 0 ) & ( 2 , 1 )**

**....... (2)**

Now from given graph is **clear line 1 contain the given point and area shaded by it is toward origin then we have less than equal sign,**

⇒ x + 2y ≤ 4

Line 2 is dotted line. So,** it does not contain the given point and area shaded by it is toward 4th quadrant then we have greater than sign in it.**

⇒ 2x - y > 0

Therefore, **The system of Linear equation is x + 2y ≤ 4 and 2x - y > 0**

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